
theorem
  449 is prime
proof
  now
    449 = 2*224 + 1; hence not 2 divides 449 by NAT_4:9;
    449 = 3*149 + 2; hence not 3 divides 449 by NAT_4:9;
    449 = 5*89 + 4; hence not 5 divides 449 by NAT_4:9;
    449 = 7*64 + 1; hence not 7 divides 449 by NAT_4:9;
    449 = 11*40 + 9; hence not 11 divides 449 by NAT_4:9;
    449 = 13*34 + 7; hence not 13 divides 449 by NAT_4:9;
    449 = 17*26 + 7; hence not 17 divides 449 by NAT_4:9;
    449 = 19*23 + 12; hence not 19 divides 449 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 449 & n is prime
  holds not n divides 449 by XPRIMET1:16;
  hence thesis by NAT_4:14;
